a) x³ + x² + x + 1; б) y⁵ - y³ - y² + 1; в) а⁴ + 2а³ - а – 2; г) бы – 3b4 – 2b² + 6; д) а² – ab – 8a + 8b; e) ab – 3b + b² – 3a; ж) 11х – ху + 11y – x²; 3) kn - mn - n² + mk.

а) x³ + x² + x + 1 = (x³ + x²) + (x + 1) = x²(x + 1) + 1(x + 1) = (x² + 1)(x + 1)

б) y⁵ - y³ - y² + 1 = (y⁵ - y³) - (y² - 1) = y³(y² - 1) - 1(y² - 1) = (y³ - 1)(y² - 1) = (y - 1)(y² + y + 1)(y - 1)(y + 1) = (y - 1)²(y + 1)(y² + y + 1)

в) a⁴ + 2a³ - a - 2 = (a⁴ + 2a³) - (a + 2) = a³(a + 2) - 1(a + 2) = (a³ - 1)(a + 2) = (a - 1)(a² + a + 1)(a + 2)

г) b⁶ - 3b⁴ - 2b² + 6 = (b⁶ - 3b⁴) - (2b² - 6) = b⁴(b² - 3) - 2(b² - 3) = (b⁴ - 2)(b² - 3)

д) a² - ab - 8a + 8b = (a² - ab) - (8a - 8b) = a(a - b) - 8(a - b) = (a - 8)(a - b)

e) ab - 3b + b² - 3a = (ab - 3a) + (b² - 3b) = a(b - 3) + b(b - 3) = (a + b)(b - 3)

ж) 11x - xy + 11y - x² = (11x + 11y) - (xy + x²) = 11(x + y) - x(y + x) = (11 - x)(x + y)

з) kn - mn - n² + mk = (kn - mn) + (mk - n²) = n(k - m) + m(k - n)